Problem: Divide the following complex numbers: $\dfrac{10(\cos(\frac{3}{2}\pi) + i \sin(\frac{3}{2}\pi))}{\cos(\frac{1}{4}\pi) + i \sin(\frac{1}{4}\pi)}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Solution: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $10(\cos(\frac{3}{2}\pi) + i \sin(\frac{3}{2}\pi))$ ) has angle $\frac{3}{2}\pi$ and radius 10. The second number ( $\cos(\frac{1}{4}\pi) + i \sin(\frac{1}{4}\pi)$ ) has angle $\frac{1}{4}\pi$ and radius 1. The radius of the result will be $\frac{10}{1}$ , which is 10. The angle of the result is $\frac{3}{2}\pi - \frac{1}{4}\pi = \frac{5}{4}\pi$ The radius of the result is $10$ and the angle of the result is $\frac{5}{4}\pi$.